Sample Problems for Midterm 1 - Differential Equations - Fall 2007 | MATH 33B, Exams of Differential Equations

Download Sample Problems for Midterm 1 - Differential Equations - Fall 2007 | MATH 33B and more Exams Differential Equations in PDF only on Docsity! Math 33b Midterm 1 Lecture 2 Fall 2007 Name: Section: Instructions: • There are 6 problems. Make sure you are not missing any pages. • Show all work in detail or your answer will not receive credit. • Write neatly and box all answers. • No calculators, books, or notes are allowed. • Answer the questions in the spaces provided on the question sheets. If you run out of room for an answer, continue on the back of the page. • Do not use your own scratch paper. Extra scratch paper is available from the front of the room. Question Points Score 1 20 2 20 3 20 4 20 5 10 6 10 Total: 100 1. (20 points) Solve the initial value problem: t dy dt + (2t2 + 3t3)y = te−(t 2+t3), y(0) = 5 4. (20 points) Find an integrating factor for the following equation (you do not need to solve the equation): 4x2y + 2y2 + (3x3 + 4xy) dy dx = 0 Hint: It is of the form µ(x, y) = xya for some a. 5. (10 points) Solve the initial value problem: dy dx = sin(πy)(2y − 4)(y3 − 6y2 + 12y − 8), y(1) = 2 6. (10 points) Find the equilibrium solutions for the following equation, and identify them as asymptotically stable or unstable. dy dt = y2 − 5y + 6